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Robustness of Change Detection Algorithms in the Presence of Registration Errors Ashok Sundaresan, Pramod K. Varshney, and Manoj K. Arora
Abstract Accurate registration of multi-temporal remote sensing images is critical to any change detection study. The presence of registration errors in the images may affect the accuracy of change detection. In this paper, we evaluate the performance of two change detection algorithms in the presence of artificially introduced registration errors in the dataset. The algorithms considered are image differencing and an algorithm based on a Markov random field (MRF) model. Registration errors have been introduced in four different ways: only in x direction, only in y direction, in both x and y directions without any rotational misregistration, and finally in both x and y directions together with rotational misregistration. Three temporal datasets, a simulated dataset and two synthetic datasets created from remote sensing images acquired by the Landsat TM sensor, have been used in our study. The results indicate that the change detection algorithm based on the MRF model is more robust to the presence of registration errors than the image differencing method.
Introduction Change detection is a key task in remote sensing studies where temporal images acquired from spaceborne and airborne sensors are analyzed to detect changes over a period of time. Some applications of remotely sensed change detection related to Earth sciences include environmental impact assessment, flood damage assessment and land-use and land-cover change analysis. Assessment of change is also important for military applications like surveillance of a particular area, target detection, and damage assessment. The basic principle of change detection from remote sensing images is based on the difference in reflectance or intensity values between the images taken at two different times due to changes on the Earth’s surface. Some commonly used image change detection algorithms are image differencing, image ratioing, image regression, principal component analysis (PCA), and change vector analysis. A review of these algorithms may be found in Singh (1989) and Jensen (2005). A necessary requirement for change detection from remote sensing images is the accurate registration of temporal images. In other words, the images must be aligned with each other such that corresponding locations in the images
Ashok Sundaresan and Pramod K. Varshney are with the Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY, 13244 (asundare @syr.edu,
[email protected]). Manoj K. Arora is at the Department of Civil Engineering, I I T Roorkee, Roorkee, 247 667, India (
[email protected]). PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
are present at identical pixel positions. A registration accuracy of less than one-fifth of a pixel has been recommended to achieve a change detection error within 10 percent (Dai and Khorram, 1998). Any registration errors (or misregistration) present in the images may lead to incorrect change detection. Due to its paramount importance as a pre-processing step for applications like change detection and image fusion, image registration has been an active area of research for many years and a number of new image registration algorithms have been developed (e.g., Brown, 1992; Zitova and Flusser, 2003). The effect of registration errors on change detection has earlier been studied by Townshend et al. (1992) and Dai and Khorram (1998). However, their conclusions and recommendations are based on only one possible type of misregistration (i.e., translation in both x and y directions). Also, no relative comparison of the performance of different change detection algorithms in the presence of registration errors has been performed, as the studies are based on a particular algorithm devised only by them. In this paper, we analyze the effect of misregistration in more detail, taking into account the effect of all possible types of misregistration on two change detection algorithms: the conventional image differencing method and a Markov random field (MRF) based change detection algorithm.
Change Detection Algorithms Used Image Differencing (ID) Image differencing is a widely used change detection algorithm due to the simplicity in its understanding and implementation. In image differencing, one image is subtracted from another image of the same area acquired at different times. The difference of intensity values is stored as a third image in which features (pixels) with no change will have near-zero values. The third image is subjected to a threshold in such a way that pixels showing change have a value one, and the pixels with no change have a value zero, thereby creating a binary change image. The determination of threshold values is still an active area of research and has not been investigated here. The readers may refer to papers on this subject (Rosin, 1997; Rosin and Ioannidis, 2003). The problem of change detection can be considered as a binary hypotheses test. Based on such an approach, methods from detection theory have recently been proposed for automatic determination of a decision threshold for classification of the
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difference image into changed and unchanged pixels (Figure 1) (Bruzzone and Prieto, 2000). In this paper, the threshold for change detection in the implementation of the image differencing algorithm is determined using Bayes’ formulation, and in particular, the minimum probability of error detection as considered by Bruzzone and Prieto (2000). Formulating change detection as a binary hypotheses testing problem, we define the following two hypotheses: H0 : d(i,j), no change at location (i,j) H1 : d(i,j), change at location (i,j) where d(i,j) is the intensity value of a pixel in the difference image at the location (i,j). It is assumed that the conditional probability density functions under the two hypotheses are Gaussian and can be written as given below:
p(X&H0)
p(X&H1)
2 exp (X m0) 2 s0 2p 2s0 √
1
2 1 exp (X m 1) 2 s1 2p 2s1 √
(1)
(2)
where, i and i, i 0,1 are the mean and variance, respectively, under Hi and x is the intensity value of a pixel. The method first involves estimating the means and variances of the two Gaussian densities after which the threshold for change detection is evaluated by solving the equation: p(X&H1) p(H0) p(X&H0) p(H1)
(3)
with respect to the variable X. P(H0) and P(H1) are the prior probabilities of unchanged and changed pixels, respectively. Substituting the expressions for the conditional probability densities and after simplification the equation that needs to be solved is the following quadratic equation,
s21 s20X 2 2 m1s20
m0s21 X m20 s21 m21 s20
2s20 s21 log
) 0 ss P(H P(H ) 1
0
0
1
(4)
Markov Random Field Model based Change Detection (MRFCD) The image differencing method considers the information contained within a pixel alone even though intensity values of neighboring pixels in an image are known to have significant correlation. Also, changes are more likely to occur in connected regions than at disjointed or isolated locations (i.e., pixels in case of remote sensing images). Therefore, MRF model-based change detection algorithms may be more appropriate than image differencing and allied algorithms. An MRF model for images exploits the statistical correlation of intensity values among neighboring pixels. The MRF-based change detection algorithm used in the study is detailed in Kasetkasem and Varshney (2004), which is a variation of the algorithm described in Bruzzone and Prieto (2000). As a first step, a difference image is obtained from the two temporal images. Then, two thresholds, one lower (T1) and one upper (T2) are selected as shown in Figure 2. These thresholds are given by: T1 MD (1 a) T2 MD (1 a)
(5)
where MD is the median value of the intensities represented as the histogram, and is the ratio of distance between the two thresholds. The value of is determined empirically based on some experimentation. The pixels in the difference image that are below the lower threshold and those that are above the upper threshold are classified as absolute unchanged and changed pixels, respectively. There is some amount of ambiguity in classifying the pixels, whose difference in intensity values are between the two thresholds, i.e., the pixels cannot be classified as changed or unchanged with complete confidence. These ambiguous pixels are further examined and classified for change or no change using an MRF model. A second-order neighborhood system wherein the eight pixels surrounding a given pixel form its neighbors is utilized by the MRF model. Depending upon the spatial dependence of a pixel upon its neighbors, further classification of the pixel as changed or unchanged is carried out. Under the MRF model, the probability density function (PDF) of the intensity level of a pixel given the intensity values of the rest of the pixels in an image is the same as the PDF of the intensity level of the pixel given its neighbors. Further, the PDF of the intensity level of a pixel is assumed to be independent of the PDFS of intensity levels of all other pixels excluding itself and its neighboring pixels.
The resulting threshold is then used to form the binary change image.
Figure 1. Assumed probability density function (PDF) of the changed and unchanged pixels in the difference image.
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Figure 2. Histogram of the absolute difference image (Equation 5) and thresholds T1 and T2.
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Effect of Image Misregistration on Change Detection Image registration is the process of aligning two images such that the same pixel coordinates represent the same locations in both images. The methods for image registration may broadly be classified as feature-based and intensity-based methods. Feature based methods are the most widely used and involve extraction of geometric features, also known as ground control points (GCP) such as intersections, landmarks clearly visible in both images. Registration of images is then performed through transformation parameters estimated by matching of GCPs in the two images. Intensity-based methods involve maximization of a similarity measure computed from the intensity values of the two images. Some commonly used similarity measures are the cross-correlation or correlation ratio, sum of squared differences (Brown, 1992) and mutual information (Chen et al., 2003). The accuracy of registration is specified in terms of RMS error. The lower the RMS error, the higher the registration accuracy. The registration errors may get manifested in the images due to image translation, rotation or both. Translational misregistration signifies a shift either in x direction or in y direction, or both. Rotational misregistration results when one of the images is rotated in either clockwise or anticlockwise direction with respect to the other. The consequences of misregistration on change detection are two-fold. First, the actual change may not be detected, i.e., a changed pixel may be classified as an unchanged pixel, which is called an omission error (or missed alarm). Secondly, an unchanged pixel may be detected as a changed one, which is termed a commission error (or false alarm). The occurrence of misses and false alarms results in decrease of change detection accuracy. Since registration errors may not be completely removed from the images, robustness of the change detection algorithms needs to be evaluated in their presence. Assuming that most of the widely used registration algorithms are able to register the images to sub-pixel accuracy, we have decided to introduce misregistration amounting to a fraction of pixel to evaluate the performance of the change detection algorithms, and thus limit the maximum amount of misregistration to 1 pixel RMS error.
Synthetic Dataset 1 A sample of Landsat TM image (size 200 200 pixels) acquired in 1995 (time t1) was used to synthetically generate another image (assumed to be taken at time t2) by introducing artificial changes (manually) in the first image. These images and the ground truth image representing the actual change (introduced artificially) between the two images are shown in Figure 4. The t1 image is assumed as the source image and t2 image as the target image. The target image contains artificial changed intensity values, in the range between 0 and 5, at the locations specified as changed in the ground truth image, which are shown as white. Synthetic Dataset 2 A small portion (size 500 500 pixels) of the Landsat TM image acquired in 1995 is considered as the source image (time, t1). The source image was then used to synthetically generate another image (assumed to be taken in time, t2) by introducing noise in the first image. The noise is modeled as a two-dimensional Poisson distribution and is introduced at random locations. The two images and the corresponding ground truth for change are shown in Figure 5. Methodology The images in the simulated and synthetic datasets contain no registration errors. One of the images in each dataset is considered as the source image and the other as the target image. Registration errors were then artificially introduced in the target image to examine their effects on change detection. The registration errors were introduced in four ways: 1. Misregistration in x direction: The target image is shifted in the x direction sequentially in steps of 0.2 pixels, while keeping the source image unaltered. 2. Misregistration in y direction: The target image is shifted in the y direction in steps of 0.2 pixels. 3. Misregistration in both x and y directions: The target image is shifted in both x and y directions simultaneously. Random amounts of shift are introduced in both the x and y
Experimental Investigations Description of Datasets Three datasets, one simulated and two synthetic, were used to experimentally evaluate the effect of misregistration on change detection. Simulated Dataset Two simulated images (representing the temporal images at times t1 and t2) and the ground truth representing the actual change between the two images were used (Figure 3). The size of the simulated dataset is 128 128 pixels. More details on this dataset can be found in Kasetkasem and Varshney (2002).
Figure 3. Simulated dataset used for experimental investigations.
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Figure 4. Synthetic dataset 1 used for experimental investigations.
Figure 5. Synthetic dataset 2 used for experimental investigations.
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directions but amounting to a particular value of RMS error, in steps of 0.2 pixels starting from 0 up to 1 pixel RMS. 4. Misregistration in both x and y directions together with rotational error: The target image is rotated in the clockwise direction in steps of 0.2 degrees from 0 degree up to 1 degree. Prior to rotation, the image is also shifted in both x and y directions amounting to a particular RMS error.
Simple linear interpolation has been used to compute the intensity values at the new pixel locations obtained due to shifts in all the cases. Once the images are misregistered, change detection is performed using the two algorithms, and the effect of registration error on change detection is assessed. After every case of misregistration (or shift), the target image is regenerated to evaluate the change detected by the two algorithms. As mentioned before, there may be two kinds of errors present due to the effect of misregistration on change detection, namely missed alarms and false alarms. To characterize the performance of each algorithm, it is necessary to quantitatively evaluate the presence of these two types of errors after every step of misregistration. For this purpose, three performance measures are used: probability of correct change detection, probability of false alarm, and probability of total error. Probability of Correct Detection PR(CD) This is defined as the ratio of the total number of pixels correctly detected as changed to the total number of pixels that have changed in the ground truth image. Probability of False Alarm PR(FA) This is defined as the ratio of the number of unchanged pixels that are wrongly detected as changed (commission error) to the total number of pixels that have not changed in the ground truth image. Probability of Total Error PR(E) This is defined as the ratio of the total number of pixels in error, changed pixels detected as unchanged (omission error), and unchanged pixels detected as changed (commission error), to the total number of pixels in the entire image. In our results, we have described the variation of these three performance measures with increasing registration error.
Results and Discussion The results obtained from three datasets are described separately. Effect of Misregistration on Change Detection for the Simulated Dataset The registration errors are introduced in the dataset by the methodology described earlier, and the performance of the two change detection algorithms is evaluated. The resulting values of the three performance measures are shown in the form of plots in Figure 6a through 6l, and the change images obtained from each algorithm at every step of misregistration are depicted in Table 1 for the purpose of visual evaluation. The change images depicted are for misregistration in both x and y directions. The change images depict the relative accuracy of the change detected by the change detection algorithms with increase in registration error. To quantify the performance of each change detection algorithm, we compare the values of the performance measures for each algorithm at an RMS registration error of 0.4 pixel. At 0.4 pixel shift, the PR(CD) values for ID are 0.5203, 0.5133, and 0.5041 for misregistration in x direction, y direction, and both x and y directions, respectively. On the other hand, the corresponding values for MRFCD are 0.8865, 0.8698, and 0.8713. At 0.4 pixel shift, the PR(FA) 378
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values for ID are 0.0312, 0.0306, and 0.0319 misregistration in x direction, y direction, and both x and y directions, respectively, while the corresponding values of MRFCD are 0.0034, 0.0041, and 0.0037. For comparison of the overall performance of change detection in presence of registration errors, we consider the PR(E) values of both algorithms. For ID, the PR(E) values for misregistration in x direction, y direction and both x and y directions, amounting to an RMS error of 0.4 pixels are 0.1313, 0.1324, and 0.1354. The corresponding PR(E) values for MRFCD are 0.0280, 0.0323, and 0.0316. With the introduction of misregistration in both x and y directions with a varying rotational error, again the performance of MRFCD is superior to that of ID. Further from the plots, we notice that the error in MRF-based change detection varies slowly (as the shift increases), whereas the performance of image differencing deteriorates substantially after a sub-pixel shift of 0.2. Since the MRF model also takes into account the contextual information present in the image, the performance of MRFCD is better than ID. For the MRF algorithm utilized in this paper, we consider a second order neighborhood where each pixel is surrounded by eight neighbors. To take into account contextual information in case of ID-derived change images also, a 3 3 pixel median filter is applied to these images. This procedure, though very crude, may be assumed as equivalent to considering the neighborhood information from the change images derived from pixel by pixel change detection algorithms. The performance of the change detection algorithms is evaluated again. Comparing this with the previous results, it is observed that the quality of ID improves at lower values of registration errors and median filtering lowers the false alarms produced by ID considerably. However, by comparing the total error in change evaluated by both algorithms, we see that MRFCD still outperforms ID at higher values of registration error by giving much smaller values of PR(E). Thus, application of median filter does not improve the accuracy of ID significantly in the presence of registration errors. Effect of Misregistration on Change Detection for Synthetic Dataset 1 The registration errors are introduced in the dataset as before and the performance of the two change detection algorithms is evaluated. The results are shown in Figure 7a through 7l. First, evaluating the performance of ID, we observe that at 0.4 pixel shift, the PR(CD) values for ID are 0.9995, 0.9947, and 0.9965 for misregistration in x direction, y direction, and both x and y directions, respectively. PR(FA) and PR(E) values for ID at 0.4 pixel shift for misregistration in x direction, y direction, and both x and y directions are 0.0113, 0.0129, 0.0121, and 0.0108, 0.0126, 0.0117, respectively. At a first glance, it may seem that the probabilities of false alarm and total error for ID itself are very small and performance of ID is satisfactory even at higher values of registration errors. But these small values of error are attributed to the fact that the amount of change is this dataset is only 4.70 percent of the entire image. Hence, the values of the PR(FA) and PR(E) are relatively small owing to the small amount of change and larger image size. However, in this case it is important to realize that a false alarm probability of 0.0121 (461 pixels) and total error probability of 0.0117 (468 pixels) is quite high if we consider the fact that total change that has taken place itself is only 4.70 percent. Hence, from the plots, it is clear that the error introduced by ID substantially increases at higher values of registration error whereas MRFCD gives better change detection performance than ID even at higher values of registration errors. At 0.4 pixel shift, the probabilities of correct detection for MRFCD are 0.9980, 0.9976, and 0.9970 for misregistration in x direction, y direction, and both x and y directions, respectively. For the same registration error, the probability of false alarm is PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
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Figure 6. (a) Probability of correct detection for misregistration in x direction using simulated dataset, (b) Probability of false alarm for misregistration in the x direction using simulated dataset, (c) Probability of total error for misregistration in the x direction using simulated dataset, (d) Probability of correct detection for misregistration in y direction using simulated dataset, (e) Probability of false alarm for misregistration in the y direction using simulated dataset, (f) Probability of total error for misregistration in the y direction using simulated dataset, (g) Probability of correct detection for misregistration in both x and y directions using simulated dataset, (h) Probability of false alarm for misregistration in both x and y directions using simulated dataset, (i) Probability of total error for misregistration in both x and y directions using simulated dataset, (j) Probability of correct detection for rotational error with misregistration in both x and y directions using simulated dataset, (k) Probability of false alarm for rotational error misregistration in both x and y directions using simulated dataset, and (l) Probability of total error for rotational error with misregistration in both x and y directions using simulated dataset.
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TABLE 1.
Registration error (RMS)
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CHANGE IMAGES OBTAINED FROM ID, ID WITH SMOOTHING AND MRFCD FOR MISREGISTRATION BOTH X and y DIRECTIONS WITH THE SIMULATED DATASET Change Image Obtained from ID
Change Image from ID with Smoothing
IN
Change Image Obtained from MRFCD
0
0.2
0.4
0.6
0.8
1.0
0.0011, 0.0011, and 0.0013 (49 pixels), and the probability of total error is 0.0011, 0.0013, and 0.0014 (56 pixels) for misregistration in x direction, y direction, and both x and y directions, respectively. For the final case of rotational and translational misregistration, it can be seen that the false alarm and total error probabilities obtained from MRFCD are much less than those obtained from ID with a slight loss of detection probability. It is also seen that median filtering of the change image obtained from ID does increase the accuracy of the final change image but is still inferior compared to the performance obtained from MRFCD. Effect of Misregistration on Change Detection for Synthetic Dataset 2 The experiments carried out earlier are repeated for the synthetic dataset 2. The performance of both ID and MRFCD is again compared when all four types of misregistration errors are present and the results are shown in Figure 8a through 8l. 380
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The values of the performance measures are compared and it is evident from the plots that the performance of MRFCD is superior to ID at all registration errors and for all types of misregistration. At a registration error of 0.8 pixel in the x direction, y direction, and both x and y directions, PR(CD) with ID equals 0.7301, 0.7440, and 0.7455, respectively, whereas from MRFCD, the corresponding values of PR(CD) is 0.8334, 0.8559, and 0.8501 for same amount of error. The PR(FA) and PR(E) values obtained from ID are 0.0259, 0.0278, 0.0266, and 0.0448, 0.0455, 0.0442 with a registration error of 0.8 pixels in the x direction, y direction, and both x and y directions, respectively, and these values increase substantially with increase in magnitude of the registration error. On the other hand, PR(FA) and PR(E) values obtained from MRFCD at 0.8 pixel error for misregistration in x direction, y direction, and both x and y directions are only 0.0032, 0.0014, 0.0031, and 0.0158, 0.0124, and 0.0144. PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
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Figure 7. (a) Probability of correct detection for misregistration in x direction using synthetic dataset 1, (b) Probability of false alarm for misregistration in the x direction using synthetic dataset 1, (c) Probability of total error for misregistration in the x direction using synthetic dataset 1, (d) Probability of correct detection for misregistration in y direction using synthetic dataset 1, (e) Probability of false alarm for misregistration in the y direction using synthetic dataset 1, (f) Probability of total error for misregistration in the y direction using synthetic dataset 1, (g) Probability of correct detection for misregistration in both x and y directions using synthetic dataset 1, (h) Probability of false alarm for misregistration in both x and y directions using synthetic dataset 1, (i) Probability of total error for misregistration in both x and y directions using synthetic dataset 1, (j) Probability of correct detection for rotational error with misregistration in both x and y directions using synthetic dataset 1, (k) Probability of false alarm for rotational error misregistration in both x and y directions using synthetic dataset 1, and (l) Probability of total error for rotational error with misregistration in both x and y directions using synthetic dataset 1.
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Figure 8. (a) Probability of correct detection for misregistration in x direction using synthetic dataset 2, (b) Probability of false alarm for misregistration in the x direction using synthetic dataset 2, (c) Probability of total error for misregistration in the x direction using synthetic dataset 2, (d) Probability of correct detection for misregistration in y direction using synthetic dataset 2, (e) Probability of false alarm for misregistration in the y direction using synthetic dataset 2, (f) Probability of total error for misregistration in the y direction using synthetic dataset 2, (g) Probability of correct detection for misregistration in both x and y directions using synthetic dataset 2, (h) Probability of false alarm for misregistration in both x and y directions using synthetic dataset 2, (i) Probability of total error for misregistration in both x and y directions using synthetic dataset 2, (j) Probability of correct detection for rotational error with misregistration in both x and y directions using synthetic dataset 2, (k) Probability of false alarm for rotational error with misregistration in both x and y directions using synthetic dataset 2, and (l) Probability of total error for rotational error with misregistration in both x and y directions using synthetic dataset 2.
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Although, the values of PR(FA) and PR(E) obtained from MRFCD also increase with an increase in registration error, but their magnitude is much smaller than that obtained from ID at same values of error. Also, in the final case of rotational misregistration along with translational misregistration, though the false alarm probability resulting from ID decreases with the help of a smoothing filter, the total error probability from MRFCD is still lesser than ID. Thus, in this case also the performance of ID decreases significantly with increase in registration error whereas MRFCD is tolerant at significantly high registration errors too.
Conclusions An experimental study to examine the robustness of two change detection algorithms, image differencing and MRFbased change detection, in the presence of registration errors in remote sensing images has been conducted in this paper. The results on a set of simulated and synthetic datasets show that for a satisfactory performance of image differencing, the amount of registration error should be no more than 0.2 pixel (RMS). On the other hand, the performance of the MRF-based change detection algorithm is satisfactory even when higher amounts of registration errors are present. With increase in registration error, the increase in probability of false alarm and probability of total error obtained from MRFCD increases at a rate much smaller than that obtained from ID. Even the use of a median filter to smooth the change image obtained from ID performs significantly inferior than the MRF based algorithm. We therefore conclude that the MRF-based change detection algorithm is much more robust to the presence of registration errors than image differencing.
Acknowledgments This is a modified and extended version of the paper presented at the ASPRS 2004 Annual Conference titled “Mountains of Data.” The work is supported by NASA under grant number NAG5 – 11227. The authors would also like to thank the anonymous reviewers for their various comments and suggestions.
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References Brown, L.G., 1992. A survey of image registration techniques, ACM Computing Surveys, 24:325–376. Bruzzone, L., and D.F. Prieto, 2000. Automatic analysis of difference image for unsupervised change detection, IEEE Transactions on Geoscience and Remote sensing, 38:1171–1182. Chen, H., P.K. Varshney, and M.K. Arora, 2003. Performance of mutual information similarity measure for registration of multitemporal remote sensing images, IEEE Transactions on Geoscience and Remote Sensing, 41:2445–2454. Dai, X., and S. Khorram, 1998. The effects of image misregistration on the accuracy of remotely sensed change detection, IEEE Transactions on Geoscience and Remote sensing, 36: 1566–1577. Jensen, J.R., 2005. Introductory Digital Image Processing, 3rd edition, Upper Saddle River, Prentice-Hall, Inc., New Jersey, 525 p. Kasetkasem, T., and P.K. Varshney, 2002. An image change detection algorithm based on Markov random field models, IEEE Transactions on Geoscience and Remote Sensing, 40: 1815–1823. Kasetkasem, T., and P.K. Varshney, 2004. Image change detection and fusion using MRF Models, Advanced Image Processing Techniques for Remotely Sensed Hyperspectral Data (P.K. Varshney and M.K. Arora, editors), Springer Verlag. Rosin, P.L., 1997. Thresholding for Change Detection, Technical Report ISTR-97-02, Brunel University. Rosin, P.L., and E. Ioannidis, 2003. Evaluation of global image thresholding for change detection, Pattern Recognition Letters, 24:2345–2356. Singh, A., 1989. Digital change detection techniques using remotely-sensed data, International Journal of Remote Sensing, 10:989–1003. Townshend, J.R.G., C.O. Justice, and C. Gurney, 1992. The impact of misregistration on change detection, IEEE Transactions on Geoscience and Remote Sensing, 30:1054–1060. Zitova, B., and J. Flusser, 2003. Image registration methods: A survey, Image and Vision Computing, 21:977–1000.
(Received 31 May 2005; accepted 24 October 2005; revised 15 November 2005)
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